Abstract：

Ordinary Differential Equations (ODEs) and Stochastic Differential Equations (SDEs) are widely used to model dynamic systems in various scientific fields such as physics, biology, finance and engineering. In recent years, ODEs/SDEs have garnered increasing attention within the machine learning community. Existing works mostly focus on tasks such as trajectory forecasting and parameter estimation. However, identifiability analysis of these systems, that is uncovering the mathematical rules governing these systems from noise-free observations, remains relatively underexplored. Solving this task holds the great promise of fully understanding the causal interactions within these systems and being able to make reliable causal inferences under interventions. In this talk, I shall present two recent contributions from our research endeavors. These contributions provide a systematic study of identifiability analysis pertaining to both linear ODEs and linear SDEs, respectively. Specifically, we derive sufficient conditions that are fully built on system parameters and the initial states, which enable the identification of the linear ODEs/SDEs. In doing so, our work not only contributes to the theoretical foundation of these dynamic systems but also lays the groundwork for reliable causal inference within this domain.